What do we mean when we say it today?
We've already pointed out that we've added an "s" to this heartfelt phrase in our modern use of it. But we've done more than that. We've changed the phrase to mean that we're choosing one of our many hearts. We're pretty sure that doesn't make as much sense. Whether we're talking literally or metaphorically, we just have one heart. That's why it's so vital to us.
But we still use this phrase to mean the same notion as the Danish prince. Hamlet means the core of his heart, and that's essentially what we're saying when we use it today. It's something we're really certain about. We're sure this happened. We know it in our heart of hearts.